Ferroelectrics Physical Effects Part 12 pdf

18 Ferroelectric Liquid Crystals Composed of Banana-Shaped Thioesters Stanisław Wróbel 1 , Janusz Chruściel 2 , Marta Wierzejska-Adamowicz 1 , Monika Marzec 1 , Danuta M. Ossowska-Chruściel 2 , Christian Legrand 3 and Redouane Douali 3 1 Institute of Physics, Jagiellonian University, Kraków 2 Institute of Chemistry, Siedlce University of Natural Sciences and Humanities, Siedlce 3 Université du Littoral Côte d'Opale, LEMCEL, Calais 1,2 Poland 3 France 1. Introduction Thermotropic liquid crystals composed of rod like molecules are known as calamitic liquid crystals. Flatten molecules of some organic compounds form discotic liquid crystals. Both kinds of compounds may exhibit nematic phase. Calamitic mesogens may also form lamellar smectic structures being so important for living systems, whereas discotic molecules make columnar mesophases. Banana-shaped (bow-shaped or bent-core) ferroelectric liquid crystals have been discovered in the last decade of the 20-th century (Noiri et al., 1996). Since then there has been a great interest in their dielectric and electro- optic properties due to potential applications (Sekine et al., 1997; Link et al., 1997; Pelzl et al., 1999). At the beginning some of the bent-core compounds were not chemically stable enough as to study them experimentally during cooling and heating runs in long lasting experiments (Wróbel et al., 2000). It came out that bent-core achiral thioesters are very stable materials showing either B 1 or B 2 phase (Rouillon et al., 2001; Ossowska-Chruściel, 2007, 2009). In this article we present complementary studies on B 1 and B 2 phases of 1,3-phenylene bis{4-[(4-alkoxybenzoyl)-sulfanyl]benzoates} (in short: nOSOR) having achiral symmetric bent-core molecules shown in Fig. 1. Fig. 1. Molecular structure of the symmetric thioester compounds studied Ferroelectrics – Physical Effects 430 (a) (b) Fig. 2. (a) Simplified model of bent-core molecule and two directors n and p, (b) Primary n and secondary p directors in the (X,Y,Z) laboratory reference frame. In B 2 phase the n director is tilted with respect to the smectic plane normal Z by the angle + θ or - θ . The n director is the average direction of the long molecular axis. The secondary director p is the average position for the short molecular in-plane axis. The other short axis is perpendicular to the (n, p) plane. Because of the tilt sign ( + or -) of the n director (Fig. 2 (b)) and two directions of the p polar director (+p and – p) there are four different structures of B 2 phase: 1. Synclinic ferroelectric (SmC S P F ) – the tilt angle is positive or negative in all smectic layers and p vectors are parallel, 2. Synclinic antiferroelectric (SmC S P A ), 3. Anticlinic ferroelectric (SmC A P F ), and 4. Anticlinic antiferroelectric (SmC A P A ). The last one shows up for two symmetric compounds (12OSOR and 14OSOR) studied in this work. A general symbol of B 2 phase can be written as follows: SmC SA P FA , where index “S” stands for synclinic, A – for anticlinic order of molecules in two neighboring layers, F – for ferroelectric and A – antiferroelectric order of polarization vectors. Banana-shaped compounds may form both lamellar and/or columnar mesophases (Szydłowska, 2003) that have become a subject of intensive experimental (Reddy & Tschierske, 2006) and theoretical studies (Vaupotič, 2006) in the last decades. In the first place research on electro-optic switching in ferro- and anti-ferroelectric phases composed of bent-core molecules has been done because of possible practical applications (Walba el al., 2000; Reddy & Tschierske, 2006). Since the discovery of ferroelectric order in smectic B phases composed of polar achiral banana-shaped molecules many experimental studies have been done that confirm ferro- or antiferroelectric order inside the layers and positive (ferroelectric) or negative (antiferroelectric) correlations between the layers. Theoretical studies were focused on inter- molecular interactions within the layers as well as interlayer correlations (Vaupotič & Čopič , 2005; Vaupotič, 2006). Liquid crystalline materials built of bent-core molecules are also attractive because they exhibit new physical properties. They possess two-dimensional smectic phases that display qualitatively different physical properties than the calamitic ferroelectric liquid crystals (Pelzl, 1999; Reddy & Tschierske, 2006). Bent–core non-chiral molecules show tendency to form a polar order within the smectic layers. Using a dielectric spectroscopy method it was found (Kresse et al., 2001, Kresse, 2003) that the reorientation of polar molecules is strongly Ferroelectric Liquid Crystals Composed of Banana-Shaped Thioesters 431 hindered in B 2 phase because of dense packing of bent-core molecules in smectic layers. Due to this the secondary order parameter (spontaneous polarization) is almost temperature independent. Thin Langmuir-Bloggett films composed of bent-core molecules studied by reversal current method (Geivandov, 2006) reveal an interesting property that polarization of nano-layers is similar to bulk polarization. Both ferro- and anti-ferroelectric order have been observed. It was also found for nano-layers that the molecules are mobile in such restricted geometry what facilitates both ferro- and antiferroelectric switching. Out of eight B phases: B 1 , B 2 , B 3 , …, B 7 , and B 8 (Reddy & Tschierske, 2006) the most thoroughly investigated seems to be the B 2 phase which may show one of four types of order depending on the sign of tilt angle (+ θ or - θ ) as well as on the sign of correlations (positive – ferroelectric order or negative – antiferroelectric order) between the polarization vectors of neighboring layers (∼P j ⋅P j+1 ). Complementary studies performed on a few homologous series show that compounds with shorter side chains (C 5 – C 9 ) exhibit only a frustrated B 1 phase, whereas those having longer chains (C 10 – C 14 ) generally display antiferroelectric B 2 phase (Bedel et al., 2000). The main objective of this article is to present dielectric and electro-optic behavior of B 1 or B 2 phases of four selected members of nOSOR series (n=8, 9, 12 and 14). The first two show only B 1 phase, and the other two with even number of carbon atoms in the side alkoxy chains display only B 2 phase of SmC A P A type. 2. Experimental methods To study phase transitions and physical properties of B 1 and B 2 phases the following complementary methods have been employed: DSC calorimetry, polarizing microscopy texture observation, linear dielectric spectroscopy, and reversal current method. Using the latter it was possible to record the reversal current spectra for the B 2 phase in form of two well separated current peaks what substantiates antiferroelectric order of this phase. As also found, the B 1 exhibits also some kind of ferroelectric order which is being gradually reduced upon temperature decreasing (Wierzejska-Adamowicz, 2010; Chruściel, 2011). 2.1 DSC calorimetric studies Thermal properties of the substances investigated have been studied by differential scanning calorimetry using Pyris1 DSC made by Perkin Elmer Company. Transition temperatures and enthalpies of the transitions have been computed based on DSC heating and cooling thermograms. Fig. 3 presents DSC results for 8OSOR compound which possesses enantiotropic B 1 phase showing up during cooling in a wide temperature range of 40 degrees. As one can see the melting process of this material is complex – on heating there are two transitions (Cr-Cr 2 -Cr 1 ) between solid modifications. Below the B 1 enantiotropic phase there seems to be an orientationally disordered crystal (ODIC). As an example endothermic and exothermic curves are shown in Fig. 4 for 12OSOR. It is seen that the B 2 phase is also enantiotropic one. On heating two crystalline modifications (Cr 1 and Cr 2 ) were found. One should point out that all compounds studied in this work are thermally very stable – their clearing points do not change after a few heating and cooling runs. Ferroelectrics – Physical Effects 432 Fig. 3. Endothermic and exothermic runs obtained by Pyris 1 DSC for 8OSOR compound Fig. 4. DSC results obtained for 12OSOR compound on cooling and heating by using Pyris1 DSC Studies of the physical properties of all compounds have been performed on cooling. The transition temperatures acquired by DSC method on cooling are as follows: 8OSOR - I 133.4 °C (16.9) → B 1 92.7 °C (14.7) → Cr 1 9OSOR - I 123.4 °C (16.0) → B 1 82.6 °C (14.0) → Cr 12OSOR - I 112.6 °C (18.5) → B 2 88.6 °C (38.7) → Cr 1 14OSOR - I 114.6 °C (17.4) → B 2 87.2 °C (57.6) → Cr Transition enthalpies for the clearing and freezing points are given in round brackets in [kJ/mol]. As seen there are small differences between the clearing and freezing enthalpies for the first two homologs with B 1 phase. Ferroelectric Liquid Crystals Composed of Banana-Shaped Thioesters 433 2.2 Electro-optic methods Texture observation and electro-optic switching between the planar and homeotropic textures for 12OSOR were done at LEMCEL using Olympus Polarizing Microscope BX60 and LINKAM temperature controller. Texture observations of 8OSOR, 9OSOR, 12OSOR, and 14OSOR were performed using Nikon Eclipse Polarizing Microscope LV100POL and INSTEC temperature controller in the Institute of Physics of the Jagiellonian University. Polarizing microscopy measurements allowed us to identify phases and to observe a planar inhomogeneous (Fig. 5(a)) and homeotropic textures of B 2 phase. The homeotropic texture (Fig. 6 (a)) was observed after applying bias field equal to 26 V p-p /µm. Figs. 5 (b) and 6 (b) present schematic molecular arrangements of the local planar and homeotropic alignments, respectively. Due to the splay deformation (Takanishi, 2003; Vaupotič, 2005) the texture is planar inhomogeneous (quasi-planar) with characteristic circular domains (Fig. 5 (a)). Under strong electric field (26 V p-p /µm) a fast transition to homeotropic texture is observed with secondary optical axis being perpendicular to the electrodes. Using triangular driving field at a certain voltage value a completely black homeotropic state was observed. Similar electro-optic behavior has been found for 14OSOR (Wierzejska-Adamowicz, 2010, Wierzejska-Adamowicz et al., 2010). (a) (b) Fig. 5. (a) Planar texture of 12OSOR’s B 2 phase obtained at T=116.8°C, U=0 V p-p /µm, AWAT HG cell – d=1.7 µm and (b) schematic local alignment of molecules in planar B 2 phase. This shows undoubtedly that there is an electro-optic switching between the two states SmC A P A →SmC S P F . Upon applying triangular voltage wave the extinction directions of the characteristic circular domains (Fig. 5 (a)) reorient clockwise or counterclockwise depending on the field direction what was observed for symmetric (Walba et al., 2000; Sadashiva et al., 2000; Zhang et al., 2006) and asymmetric (Lee et al., 2010) banana-shaped systems. However, it was not possible to grow a mono-domain of uniform planar alignment even upon applying strong electric fields. Inhomogeneous planar texture (Fig. 5 (a)) was, consisting of Maltese crosses originated from concentric layer structures,was observed. Such structures were revealed by X-ray diffraction (Takanishi, 2003). Characteristic brushes forming Maltese crosses (Ortega et al., 2004) coincide with the polarizer-analyzer positions due to anticlinic order of molecules in two neighboring layers forming a pseudo-unit cell. The authors were able to grow B 2 phase after applying a strong electric field to B 1 phase. Ferroelectrics – Physical Effects 434 (a) (b) Fig. 6. (a). Quasi-homeotropic texture of 12OSOR’s B 2 phase observed at T=116.8°C, U=26 V p-p /µm, AWAT HG cell – d=1.7 µm and (b) schematic local alignment of molecules in homeotropic B 2 phase. Electric field is parallel to the X-axis. It is worth pointing out that upon applying triangular voltage wave a completely black state (homeotropic) was observed at a certain voltage value. It is worth noting that the characteristic mosaic texture of B 1 phase does not change at all under A.C. field and electro-optic switching is not observed (Ossowska-Chruściel, D.M. et al., 2007; Wierzejska-Adamowicz, 2010). Spontaneous polarization measurements were carried out – by means of reversal current method - using 1.7 μm and 3.2 μm AWAT HG ITO cells for 9OSOR and 12OSOR, respectively. The experimental set-up consists of Fig. 7. Reversal current peaks obtained for antiferroelectric B 2 phase of 12OSOR at different driving voltages – from threshold to saturation voltage (see also Fig. 9). The real value of the driving voltage was equal to U o ×20 V p-p Agilent 3310A wave form generator, FLC Electronics amplifier F20ADI and digital scope Agilent DSO6102A. The B 2 phases of 12OSOR and 14OSOR compounds are anticlinic and antiferroelectric (SmC A P A ), so after applying to the electrodes a triangular wave two peaks are observed as Ferroelectric Liquid Crystals Composed of Banana-Shaped Thioesters 435 the current response of the sample in half a period of the driving voltage (Fig. 7). As seen in Fig. 8 spontaneous polarization of 12OSOR is very high - it reaches a value close to 600 nC/cm 2 and is weakly temperature dependent in the B 2 phase. The measurements were done applying driving electric field of 35 Vp-p/μm and frequency of 20 Hz. Spontaneous polarization of 14OSOR is slightly smaller and its temperature dependence is also weak (Chruściel, 2011) Fig. 8. Spontaneous polarization of B 2 phase vs. temperature for 12OSOR compound As seen in Fig. 9 the polarization of B 2 phase depends non-linearly on electric field. Above 30V p-p /μm it becomes saturated reaching the value of spontaneous polarization. In addition this non-linear dependence begins above the threshold field (ca. 21 Vp-p/μm at 110 ° C) Fig. 9. Polarization vs. electric field of 12OSOR’s B 2 phase at selected temperature of 110 °C As seen in Figs. 8 and 9 the B 2 phase of 12OSOR exhibits large spontaneous polarization. As found before the B 2 phases composed of bent-core asymmetric molecules (Kohout et al., 2010) show distinctly smaller spontaneous polarization (from 200 to 380 nC/cm 2 ) but upon cooling ferroelectric – antiferroelectric transition was observed. Ferroelectrics – Physical Effects 436 As known, in B 1 phase the side alkoxy chains of the molecules in one layer overlap on the cores of molecules in neighboring layers and there is a compensation of microscopic polarization (Reddy & Tschierske, 2006). However, using strong electric field one can induce polarization in this phase (Figs. 10 and 12) due to positive short range order of dipole moments inside the layers. The B 1 phase of 9OSOR shows a reasonable reversal current response (Fig. 10) which is typical for switching polarization vector from +P s to - P s in ferroelectrics. However, the temperature dependence of spontaneous polarization (Fig. 11) is not like that for a ferroelectric or antiferroelectric phase of classical ferroelectric liquid crystals (Wróbel et al., 2003). It can be treated as an induced polarization originating from molecular polar clusters created due to steric interactions inside the layers. It decreases with temperature decreasing due to inter- and/or intra-layer negative dipole-dipole correlation which are stronger at low temperatures. Fig. 10. Triangular driving voltage (right-hand side scale) applied vs. time and reversal current spectrum (left-hand side scale) of B 1 phase of 9OSOR acquired for E = 47.1 V p-p /μm, f = 5 Hz, d = 1.7 μm and at T = 100°C. The real value of the driving voltage was equal to U o ×20 V p-p Fig. 11. Polarization of 9OSOR’s ferroelectric B 1 phase vs. temperature. Measurement conditions: triangular voltage wave - E = 47.1 V p-p /μm, f = 5 Hz, d = 1.7 μm As found before by the dielectric relaxation spectroscopy, in the B 1 phase there exists antiparallel dipole-dipole correlation of transverse dipole moments (Kresse et al., 2001; Kresse, 2003). There is also a strong retardation of molecular reorientational motions at the I-B 1 (or B 2 ) Ferroelectric Liquid Crystals Composed of Banana-Shaped Thioesters 437 phase transition which is being caused by high order of bent-core molecules in B phases. Large value of the transition enthalpies for the transition between the isotropic and liquid crystalline phase of these materials as well as weak temperature dependence of the spontaneous polarization of B 2 phase also substantiate high order of B phases. As one can additionally notice the enthalpy changes of melting and freezing points (Figs. 3 and 4) are distinctly smaller than those obtained for calamitic liquid crystals what reflects a distinctly smaller change of order between liquid crystalline and crystalline phase of bent-core systems. It has been found in this study that the polarization of B 1 phase changes non-linearly with electric field applied (Fig. 12) yet it does not reach such large values as those obtained for the B 2 phase. Like for B 2 phase (Fig. 9) there is a threshold field of ca. 12 V/μm, above which a single reversal current peak shows up (Fig. 10), and above 25 V/μm the polarization of B 1 phase saturates but its value is smaller than 120 nC/cm 2 . This effect is most probably due to short range ferroelectric order and/or modulated structures (Szydłowska, 2003). Fig. 12. Polarization vs. electric field applied to the sample of 9OSOR’s ferroelectric B 1 phase. Parameters: frequency of the driving voltage - f = 5 Hz, thickness of the sample d = 1.7 μm. 2.3 Dielectric spectroscopy Dielectric measurements were done using dielectric spectrometer based on Agilent 4294A precision impedance analyzer controlled by PC using a program written on VisualStudio.NET platform. Substances were put by means of capillary action into HG - 5μm AWAT cells with gold electrodes. The dielectric spectrometer allows one to measure dielectric spectra with high accuracy. The measurements have been done using the cells with gold electrodes covered with rubbed polymer layers what facilitates planar but for banana-shaped molecules inhomogeneous alignment. The dielectric spectra were acquired in the frequency range from 40 Hz to 25 MHz. More than 60 experimental points were acquired per one frequency decade. Bias field was used to align the biaxial B 2 phase so that the polar director p is perpendicular to the electrodes. The B 2 is a biaxial phase having the dielectric permittivity tensor of the form: * 1 ** 2 * || () 0 0 ˆ () 0 () 0 00() ⊥ ⊥ ⎛⎞ εω ⎜⎟ ⎜⎟ εω= ε ω ⎜⎟ ⎜⎟ ε ω ⎝⎠ (1) Ferroelectrics – Physical Effects 438 In this study it was possible to measure two principal components of this tensor, namely * 1 () ⊥ εω and * 2 () ⊥ εω , where the latter was measured along the secondary optical axis. The difference: ε ⊥ 2 - ε ⊥ 1 ≡δε (2) can be treated as a measure of biaxiality (Lagerwall, 1998) of the B 2 phase. It has been shown by means of the dielectric spectroscopy (Ossowska-Chruściel et al., 2009; Wierzejska- Adamowicz et al., 2010; Chruściel, 2011) that with electric measuring fields being parallel to the polar director p one observes an enhanced dielectric absorption and electric permittivity as well. As found in scope of this work there is an asymmetry of the dielectric spectra between the positive and negative bias fields (Fig. 13 (a) and (b)). It means that the system studied has low point symmetry. B phases composed of bow-shaped molecules may exhibit one of the following low point symmetries: C 2V , C 2h , C 2 and even C 1 (Pelzl et al., 1999). Exemplary dielectric spectra – obtained vs. bias field - are presented in Figs. 13 (a) and (b). As seen there is an asymmetry of the dielectric spectra – the intensity of dielectric absorption depends on the sign of bias voltage. The dielectric absorption of the high frequency dielectric relaxation process is distinctly larger for negative bias fields. On the other hand, the low frequency dielectric relaxation process is being stronger enhanced for positive than negative bias fields (Fig. 13 (a)). Fig. 13. Bias field dependences of dielectric spectrum measured for B 2 phase of 12OSOR. (a) Dielectric spectra for positive and (b) negative bias voltages The B 2 phase is biaxial with the director n and polar director p. Using strong electric fields it was possible to observe in A.C. electric field transitions between a quasi-planar and homeotropic state with polar director p being normal to the electrodes. Using our HG gold cells and the experimental conditions it was not possible to study the dielectric spectrum of the B 2 phase aligned homeotropically with primary director n being parallel to electric measuring field. 2.3.1 Bias field influence The dielectric spectra were processed by using ORIGIN 7.0 software. The following complex function was fit to the experimental points measured without bias field: [...]... of the chiral dimesogenic compound and investigated the effects of terminal chain, central spacer, core structure, and chiral moiety of the chiral dimesogenic compound on appearance of the ferrielectric phase 454 Ferroelectrics – Physical Effects Fig 3 Synthetic scheme of compound (R)-I-(m,n) 3.1 Effects of the central spacer We investigated effects of parity of the central spacer of the compounds... 22) Fig 14 Dielectric spectrum of antiferroelectric B2 phase of 12OSOR obtained for planar alignment (without bias voltage) at T=95°C Dispersion and absorption curves (dashed lines) were obtained by fitting Eq (3a) to the experimental points 440 Ferroelectrics – Physical Effects Fig 15 Dielectric spectrum of antiferroelectric B2 phase of 12OSOR obtained with bias voltage (homeotropic alignment) Dispersion... switching behaviour in the Ferri-H phase 460 Ferroelectrics – Physical Effects With respect to the Ferri-L phase, its three asymmetric peaks suggest that switching between two ferroelectric states occurs via two intermediate states Figure 12 shows a model for the switching behaviour assuming that the intermediate state has three-layer periodicity Fig 12 Schematic model for electrical switching behaviour... A., Douali, R., Legrand, Ch., Chruściel, J., Sikorska, A.& Wróbel, S (2009) Planar-Homeotropic Transition Observed for B2 Phase of Banana-Shaped Thioester Phase Transit Vol 82, No 12, pp 889-898 448 Ferroelectrics – Physical Effects Pelzl, G., Diele, S & Weissflog, W (1999) Banana-Shaped Compounds – A New Field of Liquid Crystals Adv Mater Vol 11, No 9, pp.707-724 Reddy, R A & Tschierske, C (2006) Bent-core... points UB = 10 UB = 5 0.02 4.23 30.45 1.88 E-5 0.35 12. 55 2 12. 55 6.83 E-7 0.03 4.23 31.77 1.84 E-5 0.38 11.32 2 11.32 6.37 E-7 0.01 4.16 32.68 1.8 E-5 0.42 9.96 2 9.96 5.8 E-7 -0.04 4.07 33.63 1.93 E-5 0.46 9.04 2 9.04 5.39 E-7 -0.08 3.93 34.40 2.23 E-5 0.49 8.86 2 8.86 5.18 E-7 -0.10 3.77 1 UB = 15 6.78 E-7 1 UB = 20 12. 67 1 UB = 25 2 1 UB = 30 εi(∞) 12. 67 1 UB = 35 αi 0.36 1 UB [V] T = 95 oC τi [s]... Binary phase diagram between compounds (R)-I-(8,6) and (R)-I-(8,7) 3.2 Effects of the terminal chain We prepared compound (R)-I- (12, 5) possessing a decyl chain instead of an octyl chain of compound (R)-I-(8,5) and investigated its physical properties Figure 8 depicts its molecular structure and transition properties Compound (R)-I- (12, 5) shows Ferro, Ferri-H, Ferri-L, and Anti phases, as does the corresponding... (1) of ferroelectric domains, respectively Fig 16 Cole-Cole plot of the dielectric spectrum obtained at the highest bias field for 12OSOR’s antiferroelectric B2 phase Dashed lines were obtained by fitting Eq (3b) to the experimental points 442 Ferroelectrics – Physical Effects The high frequency dielectric relaxation (2) is a Debye-type process originated from the reorientation of molecules around... SmA phase but eliminates both of the Ferri-H and Ferri-L phases A phase sequence of 462 Ferroelectrics – Physical Effects SmA-Ferro-Ferri is often observed for some monomeric chiral compounds However, the ferrielectric phases of the present chiral oligomeric system are thought unlikely to coexist with a SmA phase 3.4 Effects of chirality The appearance of ferrielectric phases is known to be highly dependent... frequencies higher than 105 Hz (1/τ1) For negative bias field both these values are positive: δε1=17.25 and δε2=0.11 It is due to asymmetry of the electric permittivity tensor (Eq (1)) 444 Ferroelectrics – Physical Effects 3.3 Dielectric relaxation processes of B1 phase As found the dielectric spectra of molecular origin measured for B1 phases of 8OSOR (Ossowska-Chruściel et al., 2007) and 9OSOR (Wierzejska-Adamowicz... odd-membered dimers, however, the difference in free energy between the bent and linear conformers is such that the orientational order of the nematic phase is insufficient to convert 456 Ferroelectrics – Physical Effects bent into linear conformers Consequently, the orientational order is not enhanced and a smaller nematic-isotropic entropy is expected In the present system, compound (R)-I-(8,8) with . cooling runs. Ferroelectrics – Physical Effects 432 Fig. 3. Endothermic and exothermic runs obtained by Pyris 1 DSC for 8OSOR compound Fig. 4. DSC results obtained for 12OSOR compound. applying a strong electric field to B 1 phase. Ferroelectrics – Physical Effects 434 (a) (b) Fig. 6. (a). Quasi-homeotropic texture of 12OSOR’s B 2 phase observed at T=116.8°C, U=26 V p-p /µm,. τ i [s] α i ε i (∞) U B = 35 1 29.84 1.6 E-5 0.36 12. 67 2 12. 67 6.78 E-7 0.02 4.23 U B = 30 1 30.45 1.88 E-5 0.35 12. 55 2 12. 55 6.83 E-7 0.03 4.23 U B = 25 1 31.77 1.84 E-5